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Given the line of best fit for a set of data points with the equation y = 5x – 2.5, what is the residual for the point (4, 13)?A.13B.4.5C.–13D.–4.5

Question

Given the line of best fit for a set of data points with the equation y = 5x – 2.5, what is the residual for the point (4, 13)?A.13B.4.5C.–13D.–4.5

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Solution

To find the residual for a given point in a linear regression (line of best fit), you need to follow these steps:

  1. Plug the x-value of the point into the equation to find the predicted y-value. The equation given is y = 5x - 2.5. If we plug x = 4 into this equation, we get y = 5*4 - 2.5 = 20 - 2.5 = 17.5. So, the predicted y-value is 17.5.

  2. Subtract the predicted y-value from the actual y-value to find the residual. The actual y-value for the point (4, 13) is 13. So, the residual is 13 - 17.5 = -4.5.

Therefore, the residual for the point (4, 13) is -4.5, which corresponds to option D.

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